11 problems

For $k,\ell\in\mathbb N$ with $\ell\leq k-1$, let $c^*_{k,\ell}$ be the smallest number $c$ such that every $k$-graph $H$ on $n$ vertices with … contains a perfect fractional match…

Let $k\geq 3$ and let $G$ be a $k$-critical graph. Let $\mu(G)$ denote the matching number and $\mu_f(G)$ the fractional matching number. Fractional matching gap conjecture. If $G$…

Let $k,\ell\in\mathbb{N}$ with $1\leq \ell<k$, and define $c_{k,\ell}^{*}$ to be the smallest number $c$ such that every $k$-uniform hypergraph $H$ on $n$ vertices with … contains…

Lopsided fractional Erdős matching conjecture. For every $k$-graph $F$ and $0\leq\beta\leq 1/v(F)$,

Alon et al.'s fractional matching threshold conjecture. For all $1\leq d\leq k-1$,

Fractional Erdős matching conjecture. For integers $\ell,d\geq1$,

Let $n$, $k$, and $s$ be positive integers. For a family $\mathcal F\subset {[n]\choose k}$, let a fractional matching be a function $w:\mathcal F\to[0,1]$ such that … for every…

Let $H(n,k)=([n],E)$ be a $k$-uniform hypergraph, where $[n]=\{1,\ldots,n\}$, and let a perfect fractional matching be a collection of nonnegative real numbers…

Let $H$ be a $k$-uniform hypergraph on $n$ vertices, and let $\nu^*(H)$ be its fractional matching number: the maximum of $\sum_{e\in E(H)}w(e)$ over functions $w:E(H)\to[0,1]$ sat…

Let $f^s_0(l,m)$ denote the fractional analogue of the minimum edge threshold for forcing a fractional matching of size greater than $s$, where $l\ge2$ and $s$ is an integer with…

Let $f_d(k,n)$ denote the minimum $d$-degree forcing a fractional matching of the relevant size in a $k$-uniform hypergraph, with $1\le d\le k-1$. Fractional matching threshold con…